Equal length spring set

I hate doing unpaid shilling for deep-pocketed companies.  However, when PASCO provides exactly the right tool for teaching a physics concept, as they so often do, I can do nothing but spread the good word.

Take a look at the three springs you see in the picture to the right.  All are clearly equal in length and diameter.  They seem identical in every respect except color.

But when I hang a 500 g mass from each spring, the springs stretch different amounts.  The spring constants can be ranked, calculated, used for prediction of extension under a new load, etc.  What a great lab tool.

PASCO sells a five-spring set via the link here.  The red, blue, and yellow springs have a book value spring constant of 25 N/m, 30 N/m, and 35 N/m, respectively.  In my picture, the yellow spring is slightly less stretched than the blue one, but only slightly.  Well, that's okay, because (a) the yellow spring is supposed to have a larger spring constant than the blue spring, and (b) PASCO only lists the accuracy of each spring constant as +/- 5%.  It could well be that the blue spring is at the top edge of the 5% tolerance, or about 1.5 N/m too high; the yellow spring might be at the bottom edge of its tolerance, putting the stretch close to, but not quite, identical for each.

Now, for years I've used cheap-o springs that I bought in bulk from random sites online.  But these springs get stretched past their elastic limit, intertwined with other springs, and generally destroyed very quickly.  PASCO's set of five springs comes in a storage box, and these springs are tough to tangle.  Plus the color codes allow you to determine very quickly how carefully a lab group has done an experiment.  I'd suggest getting at least a demonstration set of these, if not a class set, unless your budget is lilliputian.

I always argue that physics equipment should be bought over many years, a few pieces at a time.  That's not the reality of most schools' budgeting processes, which generally give more money than you know what to do with all at once, but then nearly nothing for years on end.  That's simply not practical.  You want to be able to buy new toys when you find out about them; don't buy too much at once, spread your purchases out over the years.  

Well, my colleague Curtis bought a set of these, and now I'm jealous.  Good thing we ordered another set for me for next year...  Thanks, Curtis, and thanks, PASCO.

GCJ

What if my force vs. length graph for a spring is weird for small displacements?

Tim and Andy measuring the force applied by a spring

I think every physics class in the known universe does the F vs. x experiment for a spring:  The force on a spring is measured with a spring scale or hanging masses, and is plotted on the vertical axis of a graph.  The length of the spring (or the displacement from the resting position) is measured with a meterstick and plotted on the horizontal axis.  Because F = kx, the slope of this linear graph is the spring constant k.  

(As an aside, I've written up a detailed approach to this experiment for the College Board -- take a look here.)

This experiment is beautiful because the data are easy to take, and because even the worst experimenters get something resembling a line.  However, occasionally you'll see something weird -- the graph will be a line most of the way, but very small displacements will give a significantly steeper slope.  See the graph to the right (and click on it to enlarge if you can't quite see).  

What's going on?

First of all, quash the inevitable misconception:  "Oh, that makes sense because the more the spring stretched, the more force we had to use."  Well, of course -- that's what F = kx means.  We should need more force to stretch the spring for larger displacements.  

The slope of this graph represents the spring constant k, which indicates the stiffness of the spring. What's happening here is that the spring is significantly stiffer under about 3 cm of stretch.  Does that make any physical sense, though?

Well, in this case, yes.  If you get this sort of data, take a careful look at the spring you're using:

See how many of the coils are touching each other?  I asked the class to be very quiet... and then I began to stretch the spring a couple of centimeters.  We could all hear the "poing!" sounds of the individual coils unsticking from each other.  All the coils were fully separated when I had stretched the spring... about 3 cm.